We have developed a theory of the Bragg scattering for metallic nanohybrid made of an ensemble of metallic nanorods doped in a substrate. The substrate can gas, liquid or solid. An external laser field is applied to study the Bragg scattered light. The photons from the incident laser interact with the surface plasmons od nanorods and produce surface plasmon polaritons (SPPs). The incident laser field also induced dipoles in the ensemble of nanorods and they interact with each other via the dipole-dipole interaction (DDI). We have developed a theory for Bragg scattering for metallic nanohybrids using the coupled-mode formulism based on Maxwell’s equation in the presence of SPP and DDI fields. It is found that the theory of Bragg scattered depends on the susceptibility induced by the SPP and DDI fields. We used the quantum mechanical density matrix method to calculate the susceptibility. An analytical expression of the Bragg scattered light intensity is obtained. These expressions can be useful for experimental scientists and engineers who can used them to compare their experiments and make new types of plasmonic devices. Next, we have compared our theory with the experiment data for a nanohybrid made of ensemble of Au-nanoris doped in water. We found a good agreement between theory and experiments. We have also performed the numerical simulations to study the effect of SPP and DDI fields on the Bragg intensity. We have predicted an enhancement the Brag intensity due to the SPP and DDI couplings. The enhancement is due to the two extra scattering mechanisms of the SPP and DDI polaritons with acoustic phonons. We have also found that the one peak in the Bragg intensity can be split int many peaks due the SPP coupling, DDI coupling and phase factor. The splitting is due the Bragg factor appearing in the theory, and it includes the coupling of the incident laser, SPP and DDI electric fields with of acoustic phonons. The enhancement effect can be used to fabricate new types of nanosensors. Similarity, splitting phenomenon can be used to fabricate new types nanoswitches where one peak can be considered as the OFF position and many peaks can be considered as the ON position.

中文翻译：

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等离子体纳米杂化物中偶极-偶极相互作用存在下的布拉格散射研究

我们开发了一种金属纳米杂化物的布拉格散射理论，该金属纳米杂化物由掺杂在基底中的金属纳米棒集合体制成。基质可以是气体、液体或固体。应用外部激光场来研究布拉格散射光。来自入射激光的光子与纳米棒的表面等离子体激元相互作用并产生表面等离子体激元（SPP）。入射激光场还在纳米棒集合中感应出偶极子，它们通过偶极子相互作用（DDI）相互作用。我们在存在 SPP 和 DDI 场的情况下，使用基于麦克斯韦方程的耦合模式公式，开发了金属纳米杂化物的布拉格散射理论。研究发现布拉格散射理论依赖于SPP和DDI场引起的磁化率。我们使用量子力学密度矩阵法来计算磁化率。得到布拉格散射光强度的解析表达式。这些表达式对于实验科学家和工程师来说非常有用，他们可以使用它们来比较他们的实验并制造新型等离子体设备。接下来，我们将我们的理论与由掺杂在水中的金纳米粒子组成的纳米混合物的实验数据进行了比较。我们发现理论和实验之间有很好的一致性。我们还进行了数值模拟来研究 SPP 和 DDI 场对布拉格强度的影响。我们预测由于 SPP 和 DDI 耦合，布拉格强度会增强。这种增强是由于 SPP 和 DDI 极化子与声声子的两种额外散射机制所致。我们还发现，由于SPP耦合、DDI耦合和相位因子，布拉格强度中的一个峰可以分裂成多个峰。分裂是由于理论中出现的布拉格因子造成的，它包括入射激光、SPP和DDI电场与声声子的耦合。增强效应可用于制造新型纳米传感器。类似地，分裂现象可用于制造新型纳米开关，其中一个峰可被视为关闭位置，而多个峰可被视为开启位置。